Most young children will run after mom if she tries to leave them alone with a stranger. But kids who haven't bonded well with their mothers—psychologists call it "insecurely attached"—will stay behind with an adored security blanket, according to a study.

Richard H. Passman, a psychologist at the University of Wisconsin at Milwaukee, initially set out to determine whether children with secure attachments to their mothers were more or less likely to have a security blanket. He found no link at all between the strength of the mother-child relationship and the passionate love of a toddler for his blankie. But surprisingly, researchers did find that children who were both insecurely attached to their mothers and strongly attached to their blankies seemed to adjust better to an anxiety-producing situation. "For these children, the blanket promoted play, exploration and non-distress in their mothers' absence," Passman says.

Are these children becoming healthily independent? Or are they too emotionally detached? Passman isn't sure.

"We need to know more about how other family members and their own attachment histories play into it," says Passman, who has studied children and their security objects for three decades. The research also suggests that if mom had a beloved blankie as a tot, her child is more likely to have one too.